The number of even numbers greater than 10000 | vedclass

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(C) The given digits are $1, 2, 0, 2, 4, 2, 4$. There are $7$ digits in total,where $2$ appears $3$ times,$4$ appears $2$ times,$1$ appears $1$ time,a

Vedclass · Accepted Answer

$310$

Vedclass · Answer

(C) The given digits are $1, 2, 0, 2, 4, 2, 4$. There are $7$ digits in total,where $2$ appears $3$ times,$4$ appears $2$ times,$1$ appears $1$ time,and $0$ appears $1$ time.Total numbers of $7$ digits that can be formed is $\frac{7!}{3!2!} = 420$.Numbers starting with $0$ are not $7$-digit numbers. These are formed by arranging the remaining $6$ digits $(1, 2, 2, 2, 4, 4)$,which is $\frac{6!}{3!2!} = 60$.Total numbers greater than $1000000$ is $420 - 60 = 360$.To find the number of odd numbers,the last digit must be $1$. Fixing $1$ at the end,we arrange the remaining $6$ digits $(0, 2, 2, 2, 4, 4)$.Total arrangements = $\frac{6!}{3!2!} = 60$.Subtract cases where $0$ is at the first position: $\frac{5!}{3!2!} = 10$.So,total odd numbers = $60 - 10 = 50$.Total even numbers = (Total numbers) - (Total odd numbers) = $360 - 50 = 310$.

The number of even numbers greater than $1000000$ that can be formed using all the digits $1, 2, 0, 2, 4, 2, 4$ is

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